A statistically similar, but possibly simpler method to the current die mechanic would be to roll the same number of d4s as before, and count each as one unless it rolled a one (or four, if that's better esthetically).

In each case the average is .75 per die. But the range is smaller, and the results less variable.

Nope. Well, not looking at them individually, anyway, or without consideing some result fractional. You'd have to do something complicated like roll pairs of them.

But you can get a .666, or a .833. The latter would be to count each die as one, with the exception of those that rolled a one (or six, or whatever). That would make things even more tight, however. The .666 is, of course ignore two numbers, say one and two (or one and six as they seem to stand out more). This might be a better option, as it gets you back some of the looseness of the original system. But it's slower than the d4 .75 system or the d6 .833 because you're looking for two things.

These are mostly faster because you simply look for the failures and subtract from dice rolled. So a 6d roll comes up with one failure, and the result is a five.

Of course, I use the even/odd method which gives you an average of .50 in Synthesis, and it's used in Story Engine as well. This works very well, IMO. It is die type independent, for one, and the curve is very good as well. Looking at the difference between, say, a 5 die vs 3 die roll, we see that with the original method, you get the five die roller winning 55% of the time and with the even/odd method you get 51% (if these numbers seem low, consider that there is a significant chance of the roll being a tie). As such it's pretty close.